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International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 2, Pages 97-107
http://dx.doi.org/10.1155/S0161171203110046

An improved Bayes empirical Bayes estimator

Department of Mathematical and Statistical Sciences, University of Alberta, Alberta, Edmonton, Canada T6G 2G1

Received 27 September 2001

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Consider an experiment yielding an observable random quantity X whose distribution Fθ depends on a parameter θ with θ being distributed according to some distribution G0. We study the Bayesian estimation problem of θ under squared error loss function based on X, as well as some additional data available from other similar experiments according to an empirical Bayes structure. In a recent paper, Samaniego and Neath (1996) investigated the questions of whether, and when, this information can be exploited so as to provide a better estimate of θ in the current experiment. They constructed a Bayes empirical Bayes estimator that is superior to the original Bayes estimator, based only on the current observation X for sampling situations involving exponential families-conjugate prior pair. In this paper, we present an improved Bayes empirical Bayes estimator having a smaller Bayes risk than that of Samaniego and Neath's estimator. We further observe that our estimator is superior to the original Bayes estimator in more general situations than those of the exponential families-conjugate prior combination.